The estimation of operating costs of agricultural and forestry machineries is a key factor in both planning agricultural policies and farm management. Few works have tried to estimate operating costs and the produced models are normally based on deterministic approaches. Conversely, in the statistical model randomness is present and variable states are not described by unique values, but rather by probability distributions. In this study, for the first time, a multivariate statistical model based on Partial Least Squares (PLS) was adopted to predict the fuel consumption and costs of six agricultural operations such as: ploughing, harrowing, fertilization, sowing, weed control and shredding. The prediction was conducted on two steps: first of all few initial selected parameters (time per surface-area unit, maximum engine power, purchase price of the tractor and purchase price of the operating machinery) were used to estimate the fuel consumption; then the predicted fuel consumption together with the initial parameters were used to estimate the operational costs. Since the obtained models were based on an input dataset very heterogeneous, these resulted to be extremely efficient and so generalizable and robust. In details the results show prediction values in the test with

Nowadays lowering the resources use with practices not affecting the production rates is becoming more and more crucial due to their scarcity and the increasing competitiveness together with the raising awareness of the pressure agriculture has on the environment. An example is given by the introduction of precision farming technologies into conventional farm activities that has provided operators the opportunity to cope with in-field variability and to handle and manage the resources and information efficiently (

Several authors developed different approaches and methods for cost estimation and calculation of mechanized farming operations in relation to their specific needs.

In spite of the numerous elements of randomness illustrated above, traditional estimation of operating costs of agricultural machinery is largely based on deterministic models, which perform the same way for a given set of initial conditions (

In this study, a Partial Least Squares (PLS) multivariate statistical model was adopted to predict the fuel consumption and costs of six agricultural operations such as: ploughing, harrowing, fertilization, sowing, weed control and shredding. This prediction has been done starting from some selected parameters, which are: soil workability, non-working distance travelled, time per surface-area unit, maximum engine power, purchase price of the tractor and purchase price of the operating machinery in order to optimize crucial agricultural operations and thus increase the farm performance.

Data were collected from 2011 to 2014 in several experimental fields of CREA located in different parts of the Italian country (

The different agricultural operations are in details: ploughing (54 observations), harrowing (70 observations), fertilization (65 observations), sowing (43 observations), weed control (22 observations) and shredding (19 observations). The agricultural operations were carried out using tractors with different brand and power and operating machineries with different life time, annual machine use, repair and maintenance factor and accumulated use hours of machine (

The work times, at each agricultural operation, were recorded following the recommendations of the Italian Rural Engineering Association (AIGR), which considers the official methodology of the “Commission Internationale de l’Organisation Scientifique du Travall en Agriculture” (CIOSTA) (

The plots of land of the agricultural holdings examined differ in shape and size, geomorphology, soil composition and geographic location, as well as agronomical and administrative management. In order to significantly reduce the influence induced by this vast variability of agricultural holding characteristics, only several items of the CIOSTA method were taken into account.

Since the small area of experimental fields (about 0.5 ha) for the collection of work times (as reported by CIOSTA), only those related to the effective work time (TE) and to the tractor turn-around time (TAV) (which together represent the net time, TN) were considered. Considering the TN, the hourly operating cost of each tractor and piece of machinery used, was determined by means of specific analytical methods, and successively, the cost

The operating costs, for each agricultural operation, of the tractors and operating machineries, were identified by considering two main parameters: fixed and variable costs. The former involve the reintegration of the invested capital, the cost of capital using, and the various expenses (insurance, storage and taxes). The variable costs were related to the use of the agricultural machinery and include the expenses incurred for repairs and maintenance, fuel, lubricants and labour. Relatively to the life time and annual use for all tractors, a standard value of 15 years and 1067 hours per year respectively are considered.

The methods proposed in the bibliography are substantially similar in relation to the calculation of the fixed costs, whereas they differ in the formulas and coefficients adopted in calculating the variable costs. As far as this last item is concerned, reference has been made to a specific method (

The maximum engine power (P; kW), and the purchase price of the tractor (€) were obtained from the publication “Buyers’ guide 2013” (Guida all’acquisto 2013), edited by the Italian magazine “L’informatore Agrario” (http://www.informatoreagrario.it/ita/riviste/infoagri/13Ia19/sommario.asp).

Furthermore, it was also necessary to carry out an economic assessment of all the operating machinery (ploughs, harrows, seeders, fertiliser spreaders, etc.) used in the cultivation activities. The purchase prices of the various machines was determined when possible form the producers price list otherwise contacting specific retailers through personal communications.

The fuel consumption _{h}; kg/h) per each agricultural operation using the following formula:

where, Sc = specific fuel consumption in kg/kWh; P = maximum engine power in kW; and

Then, _{te} is the power used during effective operation and _{tav} is the power used during the turn-around operations and manoeuvres. By this way

To calculate the fuel consumption per hectare (Fc_{ha}; kg/ha) we modified

where _{e }= effective time consumed during the operation in hours; and _{tav} = time consumed during the turn-around operations and manoeuvres in hours.

The methodology used for calculating tractors and machineries operational costs, is referred to the one used by

The values used for the specific fuel consumption (Sc), and the power utilisation factor (d), related to different examined operations are reported in

A multivariate modelling approach was adopted to predict six agricultural operations, fuel consumption and costs. A two-step approach was applied.

In the first step, the fuel consumption for each agricultural operation was predicted from the first four variables: time per surface-area unit (h/ha), maximum engine power (kW), purchase price of the tractor (€) and purchase price of the operating machinery (€). Only for the ploughing fuel consumption two additional dummy variables were considered: soil workability (high = 1, low = 0); and minimization of the tractor non-working distance travelled (optimized = 0; not optimized = 1, where not optimized regards outward with ploughing and return without ploughing).

In the second step, the costs for each agricultural operation were predicted from the four above mentioned variables and the fuel consumption predicted as a result of the first step. A PLS regression approach was applied (^{2}, which is the most commonly used statistic to measure the forecasting potential of a multiple regression equation. The predictive ability of the model also depends on the number of latent vectors (LV) used. Generally, a good predictive model should have high values of the Pearson correlation coefficient (r) and low values for the root mean square error in calibration (RMSEC). The procedure calculated the ratio of percentage deviation (RPD), which is the ratio of the standard deviation of the measured data to the RMSE (

The obtained PLS models were applied to a standard sized Italian farm: <10 hectares farm with two tractors with reduced power (118 and 59 kW). This in order to calculate costs per hectare and fuel consumption for the six operations examined.

The performance of PLS models with different LVs in the determination of the fuel consumption for each agricultural operation is summarized in

The VIP scores obtained by the PLS regressions to estimate fuel consumption of the different agricultural operations are showed in

The performance of the PLS models with different LVs in the determination of the costs for each agricultural operation, is summarized in

The VIP scores obtained by the PLS regressions to estimate costs of the different agricultural operations are showed in

An example of application of the proposed model for a standard sized Italian farm (<10 hectares farm with a reduced mechanization), to calculate costs per hectare and fuel consumption for the six operations examined, is shown in

The monitoring of agricultural operations, in particular the costs and fuel consumption of the machinery, is a large important portion for the economical farm balance. In order to obtain an uniform procedure for machinery cost analysis, this study adopt standard models to predict fuel consumption and costs of six agricultural operations, such as ploughing, harrowing, fertilization, sowing, weed control and shredding, on the base of six variables.

For the first time, a two-step approach was applied to predict six agricultural operations fuel consumption and, then, from esteem fuel consumption, the costs in agricultural engineering. The following variables were used to develop a predictive model and thus for the estimation of costs and fuel consumption: time per surface-area unit; maximum engine power; purchase price of the tractor and of the operating machinery; soil workability; and non-working distance travelled. This method on one side uses fewer variables with respect to the ASAE one (

The majority of these methods is based on quantitative agricultural analysis (

Considering the correlation coefficients, the

Using this approach, it is possible to observe also the importance of the variables in the prediction with the analysis of the VIP scores. For ploughing, harrowing, fertilization, weed control, sowing and shredding, the time per surface-area unit is the most important variable in predicting fuel consumption. For ploughing, also the soil workability is an important variable in prediction. In addition, for ploughing, harrowing, sowing and weed control the fuel consumption is the most important variable in predicting costs. Equally, the time per surface-area unit is the most important variable for fertilization and shredding. Sowing showed higher values for the purchase price of the operating machinery, differently from the others. This is due to the high initial cost of purchase (ranging from €500 to €18,000) and for the oversizing in terms of technical and economic aspects of the operating machineries.

The provisional models applied to a standard Italian farm (<10 hectares farm with a reduced mechanization), showed the possibility to apply such an approach to generate scenarios different purposes, from policy makers to agricultural operators to farm contractors.

In conclusion, the obtained models being based on an input dataset very heterogeneous (in terms of field: shape, dimensions, slope, texture, surface, crop grown etc. and in terms of machines/operators) resulted to be extremely efficient and so generalizable and robust. This represents a crucial characteristic needed to transfer the approach from theory to practice.

The advantages of the proposed predictive model are related to the simplicity for the farmers and policy makers to acquire the necessary information. In fact, to calculate consumption and cost per hectare, is sufficient to know the tractor engine power, total work time, tractor and equipment price. In this way, it is possible to get the desired results, without

This approach may results extremely useful for both farmers (in terms of economic advantages,

^{a}sezione “denominazione, simbolo e unità di misura delle grandezza fondamentali relative all’impiego delle macchine in agricoltura, con particolare riguardo alle colture erbacee”